A methodology, based on linear programming (LP) is developed for obtaining the global optimum tree solution for single-source looped water distribution networks (WDNs) subjected to a single loading pattern. Initially, a multiple-link loop is considered, and it is shown that the cost-discharge curve is concavoconvex: convex for local minima corresponding to trees and concave for discharges in between. The logic is then extended to P loop networks for which the cost-discharge surface is a (P+1)-dimensional hypersurface. A tree of the looped WDN is initally selected, optimized by LP, and successfully modified, considering one loop at a time, so that the solution jumps on the hypersurface, from one local minimum to a better one. The procedure is continued until no further improvement in local optimum solution occurs; thus the final solution is the global optimum tree solution. The optimization procedure is illustrated through a one-source, 31-demand node, three-loop WDN, for which only 23 trees, out of possible 1048 trees, were required to be optimized for obtaining the global optimum tree solution. Since each link had to carry a minimum specified flow, one more iteration was carried out in the end to satisfy the minimum-flow constraint. Even though the tree solution is global optimum, the final solution satisfying the minimum-flow constraint cannot be claimed to be necessarily the global optimum. ¿ American Geophysical Union 1993